Analytical Geometry in the Cartesian Plane, Mathcounts State Competition 2023, Problem 23

Hope you’ve got sunblock because today, I wanted to start my first real blog post by introducing you to a very interesting problem involving $tan$ and angle sums.

By the end of this blogpost you should be able to…

✅ Use the equation of lines to determine their angle relative to the x and y axis

✅ Use the Triangle Sum Theorem to solve problems


Question (if you want to try it on your own)

The line L passes through the point (8, 11), and the smaller angle formed by the line L and the line y = x measures 31 degrees. What is the greatest possible degree measure of the smaller angle formed between the line L and the line y = x $\sqrt{3}$?

Solution

There are two cases but you might not see both.

First case (incorrect):

The magic is ✨ ✨

image


“Markdown” Madness Examples

What are Markdown files?

They’re files that end in .md. That’s the magic file ending, and the computer can take it from there to format the text.

Headers

Did you see Headers is bolded just above? That’s part of the magic of Markdown. I only wrote this:

#### Headers

But Github’s Markdown engine™ can convert that line into a bold Header.

The number of hashtags before the text determines how big the header will be on the page. My Hello world header/title at the top has two hashtags before it in my Markdown file (ie ## Hello world!).

I still don’t get it …

drawing

That’s okay. Maybe check out these resources:

  • https://en.wikipedia.org/wiki/Markdown [a little technical and long but definitely informative]
  • https://youtu.be/qhoXn4bIE1s [a six minute video on Markdown]

Here’s a clickable screenshot of what my Markdown looks like, and you can flip back and forth between that text and what you see on your screen for more context.

drawing


That’s all for now on Markdown. Now, let’s get into the mathemagic.


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